


Words From HongJian:


This
is the area where you may find something arisen from working on the problems
in Calculus. Now it is in the beginning stage. I hope this will grow and will
offer Calculus learning students certain help outside the classroom. Students
are the most important for making this place to grow and to become a spot
where the Calculus learning students would find helpful. Please send your
feedback and suggestions to me at hjlai@math.wvu.edu
and I will appreciate your comments very much. 








Click
the Tip to see if that will be helpful for you. All these reviews are in PDF format,
which may require an Acrobat Reader
to view them. If you do not have an Acrobat Reader,
you can download one free by clicking Acrobat Reader. 











·
Operations involving 3D vectors ·
Compute the angle between two vectors ·
Compute component of a vector a along a vector b 



·
Write the equation of a sphere ·
Compute the center and the radius of a sphere ·
Determine if two vectors are parallel or perpendicular 

·
Determine if three points are coline ·
Compute the direction cosines of a vector ·
Verify the triangle inequality 



·
Compute the cross (vector)
product of two vectors ·
Find unit vectors perpendicular to two given vectors ·
Compute areas ·
Compute volumes 

·
Compute the
equations of a line in space 


·
Determine the
relationship of two lines 


·
Write the
equation of a plane 


·
Determine the
relationship of a line and a plane ·
Find the angle
between two planes 


·
Write equations
of a line as intersections of two planes 



·
Determine the
relationship of a line and a plane (in parametric equations) ·
Determine the
relationship of two planes (in parametric equations) 


·
Show a
parametric curve is lying on a surface ·
Evaluate vector
functions ·
Find velocity
and acceleration vectors ·
Compute the
integrals of vector functions 


·
Compute the
derivative of vector functions ·
Find position
vectors ·
Show facts on
vectors 


·
Compute the arc
length of curves ·
Compute the
curvature of a curve ·
Search the
place with maximum curvature 

·
Compute unit
tangent and unit normalvectors, tangential and normal components 


·
Write an
equation for the surface generated by revolving a plane curve around an axis 


·
Determine the projection
of the intersection curve of two surfaces 


·
Convert from
one coordinate system to another 


· Convert equations from one coordinate system to another, I 


·
Convert
equations from one coordinate system to another, II 


·
Determine the
largest possible domain of a function 


·
Use limit laws
to evaluate limits ·
Determine if
the limit does not exist 


·
Compute partial
derivatives ·
Find an
equation of the tangent plane 


Tip 
·
Find the points
with horizontal tangent planes · Find the lowest or highest point of surfaces 

·
Find the
maximum and minimum values of f(x,y) over a region R 


·
Compute partial
derivatives with Chain Rule 


·
Compute the
Gradient Vector ·
Compute the
directional derivative of a function 


·
Find the
maximum directional derivatives of a function at a given point ·
Find tangent planes
with normal gradient vector 


·
Find and
classify critical points 


·
Compute the
(double integral) Riemann sum ·
Evaluate double
integrals over rectangular regions 


·
Evaluate double
integrals over general regions (and change order of integration) 


·
Compute area and
volume by evaluating double integrals 


·
Compute double
integrals in polar coordinates 


·
Compute
iterated triple integrals 


Tip 
·
Compute integrals
in cylindrical coordinates 

·
Compute
integrals in spherical coordinates 


·
Compute the
mass and the centroid and the moments of a solid 


·
Compute the
line integrals 


·
Compute the
line integrals in conservative fields and search for potential functions 


·
Compute
integrals using Green's Theorem 






If you think that this webpage has been useful in helping your study, please send a message to hjlai@math.wvu.edu to acknowledge it. Your email will support the further development of this and other similar assistance for Calculus studying students. 

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